∵f(x)=√3sin2x+cos(2x+π/3)+cos(2x-π/3)-1
=√3sin2x+cos2xcos(π/3)-sin2xsin(π/3)+cos2xcos(π/3)+sin2xsin(π/3)-1
=√3sin2x+cos2x-1
=2[(√3/2)sin2x+(1/2)cos2x]-1
=2[sin2xcos(π/6)+sin(π/6)cos2x]-1
=2sin[2x+(π/6)]-1
∴函数f(x)的周期T=2π/2
=π
已知函数f(x)=根号3sin2x+cos(2x+π/3)+cos(2x-π/3)-1,求函数的周期
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